# std::sqrt, std::sqrtf, std::sqrtl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float sqrt ( float num ); double sqrt ( double num ); long double sqrt ( long double num ); |  | (until C++23)
/*floating-point-type*/ sqrt ( /*floating-point-type*/ num ); |  | (since C++23) (constexpr since C++26)
float sqrtf( float num ); | (2) | (since C++11) (constexpr since C++26)
long double sqrtl( long double num ); | (3) | (since C++11) (constexpr since C++26)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> sqrt ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double sqrt ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes the square root of num. The library provides overloads of `std::sqrt` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::sqrt` on v_num. (See `math-floating-point` and `deduced-simd-t` for their definitions.) | (since C++26)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, square root of num (\({\small \sqrt{num} }\)√num), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in math_errhandling.

Domain error occurs if num is less than zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- If the argument is less than -0, FE_INVALID is raised and NaN is returned.
- If the argument is +∞ or ±0, it is returned, unmodified.
- If the argument is NaN, NaN is returned.

### Notes

`std::sqrt` is required by the IEEE standard to be correctly rounded from the infinitely precise result. In particular, the exact result is produced if it can be represented in the floating-point type. The only other operations which require this are the arithmetic operators and the function std::fma. Other functions, including std::pow, are not so constrained.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::sqrt(num) has the same effect as std::sqrt(static_cast<double>(num)).

### Example

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cmath>
    #include <cstring>
    #include <iostream>
    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        // normal use
        std::cout << "sqrt(100) = " << std::sqrt(100) << '\n'
                  << "sqrt(2) = " << std::sqrt(2) << '\n'
                  << "golden ratio = " << (1 + std::sqrt(5)) / 2 << '\n';

        // special values
        std::cout << "sqrt(-0) = " << std::sqrt(-0.0) << '\n';

        // error handling
        errno = 0;
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "sqrt(-1.0) = " << std::sqrt(-1) << '\n';
        if (errno == EDOM)
            std::cout << "    errno = EDOM " << std::strerror(errno) << '\n';
        if (std::fetestexcept(FE_INVALID))
            std::cout << "    FE_INVALID raised\n";
    }

Possible output:

    sqrt(100) = 10
    sqrt(2) = 1.41421
    golden ratio = 1.61803
    sqrt(-0) = -0
    sqrt(-1.0) = -nan
        errno = EDOM Numerical argument out of domain
        FE_INVALID raised

### See also

powpowfpowl (C++11)(C++11) | raises a number to the given power (\(\small{x^y}\)xy) (function)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11) | computes cube root (\(\small{\sqrt[3]{x}}\)3√x) (function)
hypothypotfhypotl (C++11)(C++11)(C++11) | computes hypotenuse \(\scriptsize{\sqrt{x^2+y^2}}\)√x2 +y2 and \(\scriptsize{\sqrt{x^2+y^2+z^2}}\)√x2 +y2 +z2 (since C++17) (function)
sqrt(std::complex) | complex square root in the range of the right half-plane (function template)
sqrt(std::valarray) | applies the function std::sqrt to each element of valarray (function template)
C documentation for sqrt

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